?sytrf

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?sytrf_aa

Computes the factorization of a symmetric matrix using Aasen's algorithm.

call ssytrf_aa(uplo, n, A, lda, ipiv, work, lwork, info)

call dsytrf_aa(uplo, n, A, lda, ipiv, work, lwork, info)

call csytrf_aa(uplo, n, A, lda, ipiv, work, lwork, info)

call zsytrf_aa(uplo, n, A, lda, ipiv, work, lwork, info)

Description

?sytrf_aa computes the factorization of a symmetric matrix A using Aasen's algorithm. The form of the factorization is A = U*T*U^T or A = L*T*L^T where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a complex symmetric tridiagonal matrix.

This is the blocked version of the algorithm, calling Level 3 BLAS.

Input Parameters

uplo

CHARACTER*1

= 'U': The upper triangle of A is stored.
= 'L': The lower triangle of A is stored.

n

INTEGER

The order of the matrix A. n ≥ 0.

A

REAL for ssytrf_aa

DOUBLE PRECISION for dsytrf_aa

COMPLEX for csytrf_aa

COMPLEX*16 for zsytrf_aa

Array, dimension (lda,n). On entry, the symmetric matrix A. If uplo = 'U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = 'L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

lda

INTEGER

The leading dimension of the array A.lda ≥ max(1, n).

lwork

INTEGER

The length of the array work.

If lwork = -1, a workspace query is assumed; the routine calculates only the optimal size of the work array and returns this value as the first entry of the work array, and no error message related to lwork is issued by XERBLA.

Output Parameters

A

REAL for ssytrf_aa

DOUBLE PRECISION for dsytrf_aa

COMPLEX for csytrf_aa

COMPLEX*16 for zsytrf_aa

On exit, the tridiagonal matrix is stored in the diagonals and the subdiagonals of A just below (or above) the diagonals, and L is stored below (or above) the subdiagonals, when uplo is 'L' (or 'U').

ipiv

INTEGER

Array, dimension (n). On exit, it contains the details of the interchanges; that is, the row and column k of A were interchanged with the row and column ipiv(k).

work

REAL for ssytrf_aa

DOUBLE PRECISION for dsytrf_aa

COMPLEX for csytrf_aa

COMPLEX*16 for zsytrf_aa

Array, dimension (max(1, lwork)). On exit, if info = 0, work(1) returns the optimal lwork.

info

INTEGER

= 0: successful exit.
< 0: If info = -i, the i^th argument had an illegal value.
> 0: If info = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

Parent topic: Matrix Factorization: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?sytrf_aa